"The inflation rate" generally means CPI-U[1] in the US or some similar "basket of goods" in other areas. So, this is correct, as we're usually looking at urban consumers, it would include rent but not housing.

As another poster mentioned, though, inflation or deflation as general concepts can refer to any price or cost that increases or decreases.

[1]: https://www.bls.gov/news.release/cpi.t01.htm